Well posedness of ODE’s and continuity equations with nonsmooth vector fields, and applications View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2017-09

AUTHORS

Luigi Ambrosio

ABSTRACT

This paper provides an overview of the theory of flows associated to nonsmooth vector fields, describing the main developments from the seminal paper (DiPerna and Lions in Invent Math 98:511–547, 1989) till now. The problem of well posedness of ODE’s associated to vector fields arises in many fields, for instance conservation laws (via the theory of characteristics) and fluid mechanics (when looking for consistence between Eulerian and Lagrangian points of view). The theory developed so far covers many classes of vector fields and, besides uniqueness, also more quantitative aspects, as stability estimates and differentiability of the flow. Detailed lecture notes on this topic are given in Ambrosio (in: Dacorogna, Marcellini (eds) Lecture Notes in Mathematics “Calculus of variations and non-linear partial differential equations” (CIME Series, Cetraro, 2005), vol 1927, pp 2–41, 2008), Ambrosio and Crippa (Lect Notes UMI 5:3–54, 2008), Ambrosio and Crippa (Proc R Soc Edinb Sect A 144:1191–1244 2014), Ambrosio and Trevisan (Ann Fac Sci Toulouse, 2016). More... »

PAGES

427-450

References to SciGraph publications

  • 2000. Hyperbolic Conservation Laws in Continuum Physics in NONE
  • 2011. Random Perturbation of PDEs and Fluid Dynamic Models, École d’Été de Probabilités de Saint-Flour XL – 2010 in NONE
  • 2015-10. Lagrangian flows driven by BV fields in Wiener spaces in PROBABILITY THEORY AND RELATED FIELDS
  • 1980-09. A system of non-strictly hyperbolic conservation laws arising in elasticity theory in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1989-10. Ordinary differential equations, transport theory and Sobolev spaces in INVENTIONES MATHEMATICAE
  • 2014. Analysis and Geometry of Markov Diffusion Operators in NONE
  • 1985-09. Measure-valued solutions to conservation laws in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2013-09. A note on interior estimates for the Monge–Ampère equation in MATHEMATISCHE ANNALEN
  • 2000-04. Invariant Measures for NLS in Infinite Volume in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2001-02. A Variational Approach for the 2-Dimensional Semi-Geostrophic Shallow Water Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1988-09. Regularity of generalized solutions of Monge-Ampère equations in MATHEMATISCHE ZEITSCHRIFT
  • 2009. Optimal Transport, Old and New in NONE
  • 2013-04. W2,1 regularity for solutions of the Monge–Ampère equation in INVENTIONES MATHEMATICAE
  • 2016-11. Steady Nearly Incompressible Vector Fields in Two-Dimension: Chain Rule and Renormalization in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1993-12. The dual Least Action Problem for an ideal, incompressible fluid in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2001-03. Renormalized Solutions to the Vlasov Equation with Coefficients of Bounded Variation in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2004-11. Transport equation and Cauchy problem for BV vector fields in INVENTIONES MATHEMATICAE
  • 2008. Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields in TRANSPORT EQUATIONS AND MULTI-D HYPERBOLIC CONSERVATION LAWS
  • 1988-02. Global Hölder estimates for equations of Monge-Ampère type in INVENTIONES MATHEMATICAE
  • 2004-03. Renormalized solutions of some transport equations with partially W1,1 velocities and applications in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 1999-02. A geometrical approach to monotone functions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathbb R^n$\end{document} in MATHEMATISCHE ZEITSCHRIFT
  • 2008. Transport Equation and Cauchy Problem for Non-Smooth Vector Fields in CALCULUS OF VARIATIONS AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
  • 2015-11. Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s13163-017-0244-3

    DOI

    http://dx.doi.org/10.1007/s13163-017-0244-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091243839


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Scuola Normale Superiore di Pisa", 
              "id": "https://www.grid.ac/institutes/grid.6093.c", 
              "name": [
                "Scuola Normale Superiore, Piazza Cavalieri 7, 56100, Pisa, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ambrosio", 
            "givenName": "Luigi", 
            "id": "sg:person.012621721115.68", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-3-540-75914-0_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000705398", 
              "https://doi.org/10.1007/978-3-540-75914-0_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-75914-0_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000705398", 
              "https://doi.org/10.1007/978-3-540-75914-0_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/jdeq.1997.3376", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002323195"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.matpur.2007.04.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004467694"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/jfan.2000.3637", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005386808"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s1631-073x(03)00330-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006292242"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s1631-073x(03)00330-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006292242"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002200050792", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006697148", 
              "https://doi.org/10.1007/s002200050792"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00375139", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006786301", 
              "https://doi.org/10.1007/bf00375139"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0362-546x(97)00536-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007308926"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160440809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008146820"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.3160440809", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008146820"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.aim.2012.07.034", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008480188"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1011727628", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-00227-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011727628", 
              "https://doi.org/10.1007/978-3-319-00227-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-00227-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011727628", 
              "https://doi.org/10.1007/978-3-319-00227-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01418336", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015090083", 
              "https://doi.org/10.1007/bf01418336"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01418336", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015090083", 
              "https://doi.org/10.1007/bf01418336"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1081/pde-120028850", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015133611"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.matpur.2010.07.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016465503"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10231-003-0082-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018434697", 
              "https://doi.org/10.1007/s10231-003-0082-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10231-003-0082-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018434697", 
              "https://doi.org/10.1007/s10231-003-0082-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2007.09.020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018895219"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03605309908821484", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019978180"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002050000124", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021053397", 
              "https://doi.org/10.1007/s002050000124"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1081/pde-200040210", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021337865"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-012-0405-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021379252", 
              "https://doi.org/10.1007/s00222-012-0405-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01404910", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021506200", 
              "https://doi.org/10.1007/bf01404910"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01404910", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021506200", 
              "https://doi.org/10.1007/bf01404910"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00440-014-0589-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021923626", 
              "https://doi.org/10.1007/s00440-014-0589-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00440-014-0589-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021923626", 
              "https://doi.org/10.1007/s00440-014-0589-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/qj.49712656413", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022181509"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/qj.49712656413", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022181509"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/jfan.1999.3430", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023329116"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0294-1449(02)00015-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024440708"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0294-1449(02)00015-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024440708"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00752112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025578444", 
              "https://doi.org/10.1007/bf00752112"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00752112", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025578444", 
              "https://doi.org/10.1007/bf00752112"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jde.2015.10.041", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025958689"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01393835", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026771304", 
              "https://doi.org/10.1007/bf01393835"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0764-4442(98)80022-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031440374"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00004237", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031617447", 
              "https://doi.org/10.1007/pl00004237"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-015-0875-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032141516", 
              "https://doi.org/10.1007/s00205-015-0875-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2016.10.030", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032549738"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1214/16-ejp4453", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032691386"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-662-22019-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033429031", 
              "https://doi.org/10.1007/978-3-662-22019-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-662-22019-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033429031", 
              "https://doi.org/10.1007/978-3-662-22019-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03605309708821265", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033550501"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00208-012-0895-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035873325", 
              "https://doi.org/10.1007/s00208-012-0895-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-004-0367-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036546922", 
              "https://doi.org/10.1007/s00222-004-0367-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-004-0367-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036546922", 
              "https://doi.org/10.1007/s00222-004-0367-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03605302.2012.669443", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037611003"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.anihpc.2015.05.005", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039579442"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-18231-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039648968", 
              "https://doi.org/10.1007/978-3-642-18231-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-18231-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039648968", 
              "https://doi.org/10.1007/978-3-642-18231-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-76781-7_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040506371", 
              "https://doi.org/10.1007/978-3-540-76781-7_1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.20371", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041106738"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03605301003646705", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041392896"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1992-1124980-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041660295"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-71050-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043936119", 
              "https://doi.org/10.1007/978-3-540-71050-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-71050-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043936119", 
              "https://doi.org/10.1007/978-3-540-71050-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00281590", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046266453", 
              "https://doi.org/10.1007/bf00281590"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0894-0347-1989-0969419-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046512744"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/pl00004691", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047295378", 
              "https://doi.org/10.1007/pl00004691"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0362-546x(95)00086-b", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047534803"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2008.05.007", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048692847"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-016-1006-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049504295", 
              "https://doi.org/10.1007/s00205-016-1006-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.crma.2010.01.018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050492608"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/03605301003657835", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052216893"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/(sici)1097-0312(199904)52:4<411::aid-cpa1>3.0.co;2-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1053221236"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s030821050002566x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054894249"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0308210505001344", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054895094"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0308210513000085", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054895552"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/sm1995v186n05abeh000039", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058201392"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/040615444", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062845267"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/06065249x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062849105"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/15m1007380", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062873341"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s0036139995294111", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062875337"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0219891613500100", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1063010689"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-01-11126-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064415252"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-04-12724-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064415512"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1512/iumj.2006.55.2793", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067513584"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2140/apde.2014.7.1179", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069059501"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/1971145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069676444"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/2118564", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069769051"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcds.2014.34.1251", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071734885"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/jems/431", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072318038"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/rmi/782", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072321118"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.5802/afst.1102", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1073135223"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/conm/368/06776", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089201302"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/00127094-2017-0032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1091640330"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/memo/1196", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1092559620"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/p375", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098881580"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2017-09", 
        "datePublishedReg": "2017-09-01", 
        "description": "This paper provides an overview of the theory of flows associated to nonsmooth vector fields, describing the main developments from the seminal paper (DiPerna and Lions in Invent Math 98:511\u2013547, 1989) till now. The problem of well posedness of ODE\u2019s associated to vector fields arises in many fields, for instance conservation laws (via the theory of characteristics) and fluid mechanics (when looking for consistence between Eulerian and Lagrangian points of view). The theory developed so far covers many classes of vector fields and, besides uniqueness, also more quantitative aspects, as stability estimates and differentiability of the flow. Detailed lecture notes on this topic are given in Ambrosio (in: Dacorogna, Marcellini (eds) Lecture Notes in Mathematics \u201cCalculus of variations and non-linear partial differential equations\u201d (CIME Series, Cetraro, 2005), vol 1927, pp 2\u201341, 2008), Ambrosio and Crippa (Lect Notes UMI 5:3\u201354, 2008), Ambrosio and Crippa (Proc R Soc Edinb Sect A 144:1191\u20131244 2014), Ambrosio and Trevisan (Ann Fac Sci Toulouse, 2016).", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s13163-017-0244-3", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136157", 
            "issn": [
              "1139-1138", 
              "1988-2807"
            ], 
            "name": "Revista Matem\u00e1tica Complutense", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "30"
          }
        ], 
        "name": "Well posedness of ODE\u2019s and continuity equations with nonsmooth vector fields, and applications", 
        "pagination": "427-450", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "40434c31e86f1b5cc7cb7d73a3c9257b186ab8de3b85e10c54f6b51c1372516c"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s13163-017-0244-3"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1091243839"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s13163-017-0244-3", 
          "https://app.dimensions.ai/details/publication/pub.1091243839"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T09:39", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000346_0000000346/records_99833_00000004.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs13163-017-0244-3"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s13163-017-0244-3'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s13163-017-0244-3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s13163-017-0244-3'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s13163-017-0244-3'


     

    This table displays all metadata directly associated to this object as RDF triples.

    317 TRIPLES      21 PREDICATES      105 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s13163-017-0244-3 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nc405d983bb294d7b9dfff9c770310ad2
    4 schema:citation sg:pub.10.1007/978-3-319-00227-9
    5 sg:pub.10.1007/978-3-540-71050-9
    6 sg:pub.10.1007/978-3-540-75914-0_1
    7 sg:pub.10.1007/978-3-540-76781-7_1
    8 sg:pub.10.1007/978-3-642-18231-0
    9 sg:pub.10.1007/978-3-662-22019-1
    10 sg:pub.10.1007/bf00281590
    11 sg:pub.10.1007/bf00375139
    12 sg:pub.10.1007/bf00752112
    13 sg:pub.10.1007/bf01393835
    14 sg:pub.10.1007/bf01404910
    15 sg:pub.10.1007/bf01418336
    16 sg:pub.10.1007/pl00004237
    17 sg:pub.10.1007/pl00004691
    18 sg:pub.10.1007/s00205-015-0875-9
    19 sg:pub.10.1007/s00205-016-1006-y
    20 sg:pub.10.1007/s002050000124
    21 sg:pub.10.1007/s00208-012-0895-9
    22 sg:pub.10.1007/s002200050792
    23 sg:pub.10.1007/s00222-004-0367-2
    24 sg:pub.10.1007/s00222-012-0405-4
    25 sg:pub.10.1007/s00440-014-0589-1
    26 sg:pub.10.1007/s10231-003-0082-4
    27 https://app.dimensions.ai/details/publication/pub.1011727628
    28 https://doi.org/10.1002/(sici)1097-0312(199904)52:4<411::aid-cpa1>3.0.co;2-3
    29 https://doi.org/10.1002/cpa.20371
    30 https://doi.org/10.1002/cpa.3160440809
    31 https://doi.org/10.1002/qj.49712656413
    32 https://doi.org/10.1006/jdeq.1997.3376
    33 https://doi.org/10.1006/jfan.1999.3430
    34 https://doi.org/10.1006/jfan.2000.3637
    35 https://doi.org/10.1016/0362-546x(95)00086-b
    36 https://doi.org/10.1016/j.aim.2012.07.034
    37 https://doi.org/10.1016/j.anihpc.2015.05.005
    38 https://doi.org/10.1016/j.crma.2010.01.018
    39 https://doi.org/10.1016/j.jde.2015.10.041
    40 https://doi.org/10.1016/j.jfa.2007.09.020
    41 https://doi.org/10.1016/j.jfa.2008.05.007
    42 https://doi.org/10.1016/j.jfa.2016.10.030
    43 https://doi.org/10.1016/j.matpur.2007.04.001
    44 https://doi.org/10.1016/j.matpur.2010.07.001
    45 https://doi.org/10.1016/s0294-1449(02)00015-x
    46 https://doi.org/10.1016/s0362-546x(97)00536-1
    47 https://doi.org/10.1016/s0764-4442(98)80022-0
    48 https://doi.org/10.1016/s1631-073x(03)00330-3
    49 https://doi.org/10.1017/s030821050002566x
    50 https://doi.org/10.1017/s0308210505001344
    51 https://doi.org/10.1017/s0308210513000085
    52 https://doi.org/10.1070/sm1995v186n05abeh000039
    53 https://doi.org/10.1080/03605301003646705
    54 https://doi.org/10.1080/03605301003657835
    55 https://doi.org/10.1080/03605302.2012.669443
    56 https://doi.org/10.1080/03605309708821265
    57 https://doi.org/10.1080/03605309908821484
    58 https://doi.org/10.1081/pde-120028850
    59 https://doi.org/10.1081/pde-200040210
    60 https://doi.org/10.1090/conm/368/06776
    61 https://doi.org/10.1090/memo/1196
    62 https://doi.org/10.1090/s0894-0347-1989-0969419-8
    63 https://doi.org/10.1090/s0894-0347-1992-1124980-8
    64 https://doi.org/10.1137/040615444
    65 https://doi.org/10.1137/06065249x
    66 https://doi.org/10.1137/15m1007380
    67 https://doi.org/10.1137/s0036139995294111
    68 https://doi.org/10.1142/p375
    69 https://doi.org/10.1142/s0219891613500100
    70 https://doi.org/10.1214/16-ejp4453
    71 https://doi.org/10.1215/00127094-2017-0032
    72 https://doi.org/10.1215/s0012-7094-01-11126-5
    73 https://doi.org/10.1215/s0012-7094-04-12724-1
    74 https://doi.org/10.1512/iumj.2006.55.2793
    75 https://doi.org/10.2140/apde.2014.7.1179
    76 https://doi.org/10.2307/1971145
    77 https://doi.org/10.2307/2118564
    78 https://doi.org/10.3934/dcds.2014.34.1251
    79 https://doi.org/10.4171/jems/431
    80 https://doi.org/10.4171/rmi/782
    81 https://doi.org/10.5802/afst.1102
    82 schema:datePublished 2017-09
    83 schema:datePublishedReg 2017-09-01
    84 schema:description This paper provides an overview of the theory of flows associated to nonsmooth vector fields, describing the main developments from the seminal paper (DiPerna and Lions in Invent Math 98:511–547, 1989) till now. The problem of well posedness of ODE’s associated to vector fields arises in many fields, for instance conservation laws (via the theory of characteristics) and fluid mechanics (when looking for consistence between Eulerian and Lagrangian points of view). The theory developed so far covers many classes of vector fields and, besides uniqueness, also more quantitative aspects, as stability estimates and differentiability of the flow. Detailed lecture notes on this topic are given in Ambrosio (in: Dacorogna, Marcellini (eds) Lecture Notes in Mathematics “Calculus of variations and non-linear partial differential equations” (CIME Series, Cetraro, 2005), vol 1927, pp 2–41, 2008), Ambrosio and Crippa (Lect Notes UMI 5:3–54, 2008), Ambrosio and Crippa (Proc R Soc Edinb Sect A 144:1191–1244 2014), Ambrosio and Trevisan (Ann Fac Sci Toulouse, 2016).
    85 schema:genre research_article
    86 schema:inLanguage en
    87 schema:isAccessibleForFree false
    88 schema:isPartOf N3918e623937545e8a150e4b6ed2a0d9d
    89 N5c2fb40220b74d9f9b65cee7c47ce5ca
    90 sg:journal.1136157
    91 schema:name Well posedness of ODE’s and continuity equations with nonsmooth vector fields, and applications
    92 schema:pagination 427-450
    93 schema:productId N18fbce3df1da4fcc915a7fbede7ffd7a
    94 N306afeda3b6c445a81c109d6528ef30e
    95 Nafab50ab1f0546068a935d2889c10476
    96 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091243839
    97 https://doi.org/10.1007/s13163-017-0244-3
    98 schema:sdDatePublished 2019-04-11T09:39
    99 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    100 schema:sdPublisher Nf42cea0d98d44514b343f9900ed2a109
    101 schema:url https://link.springer.com/10.1007%2Fs13163-017-0244-3
    102 sgo:license sg:explorer/license/
    103 sgo:sdDataset articles
    104 rdf:type schema:ScholarlyArticle
    105 N18fbce3df1da4fcc915a7fbede7ffd7a schema:name doi
    106 schema:value 10.1007/s13163-017-0244-3
    107 rdf:type schema:PropertyValue
    108 N306afeda3b6c445a81c109d6528ef30e schema:name dimensions_id
    109 schema:value pub.1091243839
    110 rdf:type schema:PropertyValue
    111 N3918e623937545e8a150e4b6ed2a0d9d schema:volumeNumber 30
    112 rdf:type schema:PublicationVolume
    113 N5c2fb40220b74d9f9b65cee7c47ce5ca schema:issueNumber 3
    114 rdf:type schema:PublicationIssue
    115 Nafab50ab1f0546068a935d2889c10476 schema:name readcube_id
    116 schema:value 40434c31e86f1b5cc7cb7d73a3c9257b186ab8de3b85e10c54f6b51c1372516c
    117 rdf:type schema:PropertyValue
    118 Nc405d983bb294d7b9dfff9c770310ad2 rdf:first sg:person.012621721115.68
    119 rdf:rest rdf:nil
    120 Nf42cea0d98d44514b343f9900ed2a109 schema:name Springer Nature - SN SciGraph project
    121 rdf:type schema:Organization
    122 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    123 schema:name Mathematical Sciences
    124 rdf:type schema:DefinedTerm
    125 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    126 schema:name Pure Mathematics
    127 rdf:type schema:DefinedTerm
    128 sg:journal.1136157 schema:issn 1139-1138
    129 1988-2807
    130 schema:name Revista Matemática Complutense
    131 rdf:type schema:Periodical
    132 sg:person.012621721115.68 schema:affiliation https://www.grid.ac/institutes/grid.6093.c
    133 schema:familyName Ambrosio
    134 schema:givenName Luigi
    135 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68
    136 rdf:type schema:Person
    137 sg:pub.10.1007/978-3-319-00227-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011727628
    138 https://doi.org/10.1007/978-3-319-00227-9
    139 rdf:type schema:CreativeWork
    140 sg:pub.10.1007/978-3-540-71050-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043936119
    141 https://doi.org/10.1007/978-3-540-71050-9
    142 rdf:type schema:CreativeWork
    143 sg:pub.10.1007/978-3-540-75914-0_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000705398
    144 https://doi.org/10.1007/978-3-540-75914-0_1
    145 rdf:type schema:CreativeWork
    146 sg:pub.10.1007/978-3-540-76781-7_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040506371
    147 https://doi.org/10.1007/978-3-540-76781-7_1
    148 rdf:type schema:CreativeWork
    149 sg:pub.10.1007/978-3-642-18231-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039648968
    150 https://doi.org/10.1007/978-3-642-18231-0
    151 rdf:type schema:CreativeWork
    152 sg:pub.10.1007/978-3-662-22019-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033429031
    153 https://doi.org/10.1007/978-3-662-22019-1
    154 rdf:type schema:CreativeWork
    155 sg:pub.10.1007/bf00281590 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046266453
    156 https://doi.org/10.1007/bf00281590
    157 rdf:type schema:CreativeWork
    158 sg:pub.10.1007/bf00375139 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006786301
    159 https://doi.org/10.1007/bf00375139
    160 rdf:type schema:CreativeWork
    161 sg:pub.10.1007/bf00752112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025578444
    162 https://doi.org/10.1007/bf00752112
    163 rdf:type schema:CreativeWork
    164 sg:pub.10.1007/bf01393835 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026771304
    165 https://doi.org/10.1007/bf01393835
    166 rdf:type schema:CreativeWork
    167 sg:pub.10.1007/bf01404910 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021506200
    168 https://doi.org/10.1007/bf01404910
    169 rdf:type schema:CreativeWork
    170 sg:pub.10.1007/bf01418336 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015090083
    171 https://doi.org/10.1007/bf01418336
    172 rdf:type schema:CreativeWork
    173 sg:pub.10.1007/pl00004237 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031617447
    174 https://doi.org/10.1007/pl00004237
    175 rdf:type schema:CreativeWork
    176 sg:pub.10.1007/pl00004691 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047295378
    177 https://doi.org/10.1007/pl00004691
    178 rdf:type schema:CreativeWork
    179 sg:pub.10.1007/s00205-015-0875-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032141516
    180 https://doi.org/10.1007/s00205-015-0875-9
    181 rdf:type schema:CreativeWork
    182 sg:pub.10.1007/s00205-016-1006-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1049504295
    183 https://doi.org/10.1007/s00205-016-1006-y
    184 rdf:type schema:CreativeWork
    185 sg:pub.10.1007/s002050000124 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021053397
    186 https://doi.org/10.1007/s002050000124
    187 rdf:type schema:CreativeWork
    188 sg:pub.10.1007/s00208-012-0895-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035873325
    189 https://doi.org/10.1007/s00208-012-0895-9
    190 rdf:type schema:CreativeWork
    191 sg:pub.10.1007/s002200050792 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006697148
    192 https://doi.org/10.1007/s002200050792
    193 rdf:type schema:CreativeWork
    194 sg:pub.10.1007/s00222-004-0367-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036546922
    195 https://doi.org/10.1007/s00222-004-0367-2
    196 rdf:type schema:CreativeWork
    197 sg:pub.10.1007/s00222-012-0405-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021379252
    198 https://doi.org/10.1007/s00222-012-0405-4
    199 rdf:type schema:CreativeWork
    200 sg:pub.10.1007/s00440-014-0589-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021923626
    201 https://doi.org/10.1007/s00440-014-0589-1
    202 rdf:type schema:CreativeWork
    203 sg:pub.10.1007/s10231-003-0082-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018434697
    204 https://doi.org/10.1007/s10231-003-0082-4
    205 rdf:type schema:CreativeWork
    206 https://app.dimensions.ai/details/publication/pub.1011727628 schema:CreativeWork
    207 https://doi.org/10.1002/(sici)1097-0312(199904)52:4<411::aid-cpa1>3.0.co;2-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053221236
    208 rdf:type schema:CreativeWork
    209 https://doi.org/10.1002/cpa.20371 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041106738
    210 rdf:type schema:CreativeWork
    211 https://doi.org/10.1002/cpa.3160440809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008146820
    212 rdf:type schema:CreativeWork
    213 https://doi.org/10.1002/qj.49712656413 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022181509
    214 rdf:type schema:CreativeWork
    215 https://doi.org/10.1006/jdeq.1997.3376 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002323195
    216 rdf:type schema:CreativeWork
    217 https://doi.org/10.1006/jfan.1999.3430 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023329116
    218 rdf:type schema:CreativeWork
    219 https://doi.org/10.1006/jfan.2000.3637 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005386808
    220 rdf:type schema:CreativeWork
    221 https://doi.org/10.1016/0362-546x(95)00086-b schema:sameAs https://app.dimensions.ai/details/publication/pub.1047534803
    222 rdf:type schema:CreativeWork
    223 https://doi.org/10.1016/j.aim.2012.07.034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008480188
    224 rdf:type schema:CreativeWork
    225 https://doi.org/10.1016/j.anihpc.2015.05.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039579442
    226 rdf:type schema:CreativeWork
    227 https://doi.org/10.1016/j.crma.2010.01.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050492608
    228 rdf:type schema:CreativeWork
    229 https://doi.org/10.1016/j.jde.2015.10.041 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025958689
    230 rdf:type schema:CreativeWork
    231 https://doi.org/10.1016/j.jfa.2007.09.020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018895219
    232 rdf:type schema:CreativeWork
    233 https://doi.org/10.1016/j.jfa.2008.05.007 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048692847
    234 rdf:type schema:CreativeWork
    235 https://doi.org/10.1016/j.jfa.2016.10.030 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032549738
    236 rdf:type schema:CreativeWork
    237 https://doi.org/10.1016/j.matpur.2007.04.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004467694
    238 rdf:type schema:CreativeWork
    239 https://doi.org/10.1016/j.matpur.2010.07.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016465503
    240 rdf:type schema:CreativeWork
    241 https://doi.org/10.1016/s0294-1449(02)00015-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1024440708
    242 rdf:type schema:CreativeWork
    243 https://doi.org/10.1016/s0362-546x(97)00536-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007308926
    244 rdf:type schema:CreativeWork
    245 https://doi.org/10.1016/s0764-4442(98)80022-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031440374
    246 rdf:type schema:CreativeWork
    247 https://doi.org/10.1016/s1631-073x(03)00330-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006292242
    248 rdf:type schema:CreativeWork
    249 https://doi.org/10.1017/s030821050002566x schema:sameAs https://app.dimensions.ai/details/publication/pub.1054894249
    250 rdf:type schema:CreativeWork
    251 https://doi.org/10.1017/s0308210505001344 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054895094
    252 rdf:type schema:CreativeWork
    253 https://doi.org/10.1017/s0308210513000085 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054895552
    254 rdf:type schema:CreativeWork
    255 https://doi.org/10.1070/sm1995v186n05abeh000039 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058201392
    256 rdf:type schema:CreativeWork
    257 https://doi.org/10.1080/03605301003646705 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041392896
    258 rdf:type schema:CreativeWork
    259 https://doi.org/10.1080/03605301003657835 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052216893
    260 rdf:type schema:CreativeWork
    261 https://doi.org/10.1080/03605302.2012.669443 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037611003
    262 rdf:type schema:CreativeWork
    263 https://doi.org/10.1080/03605309708821265 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033550501
    264 rdf:type schema:CreativeWork
    265 https://doi.org/10.1080/03605309908821484 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019978180
    266 rdf:type schema:CreativeWork
    267 https://doi.org/10.1081/pde-120028850 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015133611
    268 rdf:type schema:CreativeWork
    269 https://doi.org/10.1081/pde-200040210 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021337865
    270 rdf:type schema:CreativeWork
    271 https://doi.org/10.1090/conm/368/06776 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089201302
    272 rdf:type schema:CreativeWork
    273 https://doi.org/10.1090/memo/1196 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092559620
    274 rdf:type schema:CreativeWork
    275 https://doi.org/10.1090/s0894-0347-1989-0969419-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046512744
    276 rdf:type schema:CreativeWork
    277 https://doi.org/10.1090/s0894-0347-1992-1124980-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041660295
    278 rdf:type schema:CreativeWork
    279 https://doi.org/10.1137/040615444 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062845267
    280 rdf:type schema:CreativeWork
    281 https://doi.org/10.1137/06065249x schema:sameAs https://app.dimensions.ai/details/publication/pub.1062849105
    282 rdf:type schema:CreativeWork
    283 https://doi.org/10.1137/15m1007380 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062873341
    284 rdf:type schema:CreativeWork
    285 https://doi.org/10.1137/s0036139995294111 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062875337
    286 rdf:type schema:CreativeWork
    287 https://doi.org/10.1142/p375 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098881580
    288 rdf:type schema:CreativeWork
    289 https://doi.org/10.1142/s0219891613500100 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063010689
    290 rdf:type schema:CreativeWork
    291 https://doi.org/10.1214/16-ejp4453 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032691386
    292 rdf:type schema:CreativeWork
    293 https://doi.org/10.1215/00127094-2017-0032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091640330
    294 rdf:type schema:CreativeWork
    295 https://doi.org/10.1215/s0012-7094-01-11126-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064415252
    296 rdf:type schema:CreativeWork
    297 https://doi.org/10.1215/s0012-7094-04-12724-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064415512
    298 rdf:type schema:CreativeWork
    299 https://doi.org/10.1512/iumj.2006.55.2793 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067513584
    300 rdf:type schema:CreativeWork
    301 https://doi.org/10.2140/apde.2014.7.1179 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069059501
    302 rdf:type schema:CreativeWork
    303 https://doi.org/10.2307/1971145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069676444
    304 rdf:type schema:CreativeWork
    305 https://doi.org/10.2307/2118564 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069769051
    306 rdf:type schema:CreativeWork
    307 https://doi.org/10.3934/dcds.2014.34.1251 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071734885
    308 rdf:type schema:CreativeWork
    309 https://doi.org/10.4171/jems/431 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072318038
    310 rdf:type schema:CreativeWork
    311 https://doi.org/10.4171/rmi/782 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072321118
    312 rdf:type schema:CreativeWork
    313 https://doi.org/10.5802/afst.1102 schema:sameAs https://app.dimensions.ai/details/publication/pub.1073135223
    314 rdf:type schema:CreativeWork
    315 https://www.grid.ac/institutes/grid.6093.c schema:alternateName Scuola Normale Superiore di Pisa
    316 schema:name Scuola Normale Superiore, Piazza Cavalieri 7, 56100, Pisa, Italy
    317 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...